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Share Price Evolution as Stationary, Dependent Continuous-Time Random Walk

100%
Gubiec T., Kutner R.
Acta Physica Polonica A
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2010
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vol. 117
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issue 4
669-672
EN
Simple model of share price evolution, which is an extension of Kehr-Kutner-Binder one and Montero-Masoliver models, is presented. The market empirical data inspired the assumptions of the model. The model seems to be the reference one for the study of the short-range correlations in financial data as it considers the observed correlation over two successive jumps of the financial ant.
2
Content available remote

Reinterpretation of Sieczka-Hołyst Financial Market Model

81%
Denys M., Gubiec T., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
513-517
EN
In this work we essentially reinterpreted the Sieczka-Hołyst model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents' opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the Sieczka-Hołyst model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.
3
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Dynamic Structural and Topological Phase Transitions on the Warsaw Stock Exchange: A Phenomenological Approach

81%
Sienkiewicz A., Gubiec T., Kutner R., Struzik Z.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
615-620
EN
We study crash dynamics of the Warsaw Stock Exchange by using minimal spanning tree networks. We identify the transition of the complex network during its evolution from a (hierarchical) power law minimal spanning tree network - representing the stable state of Warsaw Stock Exchange before the recent worldwide financial crash, to a superstar-like (or superhub) minimal spanning tree network of the market decorated by a hierarchy of trees - an unstable, intermediate market state. Subsequently, we observe a transition from this complex tree to the topology of the (hierarchical) power law minimal spanning tree network decorated by several star-like trees or hubs - this structure and topology represent the Warsaw Stock Exchange after the worldwide financial crash, and can be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.
4
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Statistical Collapse of Excessive Market Losses

71%
Denys M., Jagielski M., Gubiec T., Kutner R., Stanley H.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
913-916
EN
We analytically derive superstatistics (or complex statistics) that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) exhibiting transition thresholds. We measure the interevent times between excessive losses (that is, greater than some threshold) and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates themselves and a "superscaling" configuration emerges.
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